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Block #344,487

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/5/2014, 8:26:12 AM Β· Difficulty 10.1937 Β· 6,450,981 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
eb00cb0c854bb83057a2c65a9d49ea883dafb8a1912244a5193f75489510650e
View on Chainz β†—

Height

#344,487

Difficulty

10.193703

Transactions

1

Size

204 B

Version

2

Bits

0a319685

Nonce

251,762

Timestamp

1/5/2014, 8:26:12 AM

Confirmations

6,450,981

Merkle Root

71667dd100ce4a3473c9e06c961d1dc8c26a80cd67d15939e78ffab10ca3426b
Transactions (1)
Coinbase71667dd100ce4a…8ffab10ca3426b
1 in β†’ 1 out9.6100 XPM110 B
AeKNrjNj…1NEq95Ta
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.364 Γ— 10¹⁰³(104-digit number)
73642893859985895645…94830023424452984000
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
7.364 Γ— 10¹⁰³(104-digit number)
73642893859985895645…94830023424452984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.472 Γ— 10¹⁰⁴(105-digit number)
14728578771997179129…89660046848905968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.945 Γ— 10¹⁰⁴(105-digit number)
29457157543994358258…79320093697811936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.891 Γ— 10¹⁰⁴(105-digit number)
58914315087988716516…58640187395623872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.178 Γ— 10¹⁰⁡(106-digit number)
11782863017597743303…17280374791247744001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.356 Γ— 10¹⁰⁡(106-digit number)
23565726035195486606…34560749582495488001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.713 Γ— 10¹⁰⁡(106-digit number)
47131452070390973213…69121499164990976001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.426 Γ— 10¹⁰⁡(106-digit number)
94262904140781946426…38242998329981952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.885 Γ— 10¹⁰⁢(107-digit number)
18852580828156389285…76485996659963904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.770 Γ— 10¹⁰⁢(107-digit number)
37705161656312778570…52971993319927808001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 344487

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock eb00cb0c854bb83057a2c65a9d49ea883dafb8a1912244a5193f75489510650e

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #344,487 on Chainz β†—
Circulating Supply:57,607,803 XPMΒ·at block #6,795,467 Β· updates every 60s
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